Answer
$(-4,-3),(3,4)$.
Work Step by Step
The equation of the circle: $x^2+y^2=25$ ...... (1)
The equation of the line: $y=x+1$ ...... (2)
Substitute the value of $y$ from equation (2) to equation (1).
$\Rightarrow x^2+(x+1)^2=25$
Clear the parentheses.
$\Rightarrow x^2+x^2+2x+1=25$
Subtract $25$ from each side.
$\Rightarrow 2x^2+2x+1-25=0$
Add like terms.
$\Rightarrow 2x^2+2x-24=0$
Divide the equation by $2$.
$\Rightarrow x^2+x-12=0$
Factor.
$\Rightarrow (x+4)(x-3)=0$
Use the zero product property.
$ x+4=0$ or $x-3=0$
Solve for $x$.
$ x=-4$ or $x=3$
Substitute the values of $x$ into equation (2).
For $x=-4$.
$\Rightarrow y=-4+1$
Simplify.
$\Rightarrow y=-3$
For $x=3$.
$\Rightarrow y=3+1$
Simplify.
$\Rightarrow y=4$
Hence, the points of intersection are
$(-4,-3)$ and $(3,4)$.
